Travelling Waves Chapter 20

Waves Mechanical Waves –Require a medium –Sound, water, strings Electromagnetic Waves –Can travel through a vacuum –Radio to gamma Matter Waves –Electrons and atoms

Transverse and Longitudinal Transverse –Up and down –Displacement is perpendicular to medium –Strings, water, electromagnetic Longitudinal –pulses –Displacement –Sound

Formula T = 1/f v =  f v = speed (m/s) = wavelength (m) f = frequency (cycles/s or Hz)

Example 1 A sound waves travels at 343 m/s and has a frequency of 17,000 Hz a.Convert the frequency to kiloHertz b.Calculate the wavelength

Example 2 A photon has a wavelength of 5.50 X m and a frequency of 5.45 X Hz. a.Calculate the speed of light b.Calculate the period

Speed of Sound Varies with the medium v = \/ B/  Solids and liquids –Less compressible –Higher Bulk modulus –Move faster than in air

MaterialSpeed of Sound (m/s) Air (20 o C) 343 Air (0 o C) 331 Water1440 Saltwater1560 Iron/Steel ~5000

Speed of Sound: Temperature Speed increases with temperature ( o C) v ≈ ( T) m/s What is the speed of sound at 20 o C? What is the speed of sound at 2 o C?

Speed of Sound: Example 1 How many seconds will it take the sound of a lightening strike to travel 1 mile (1.6 km) if the speed of sound is 340 m/s? v = d/t t = d/v t = 1600 m/(340 m/s) ≈ 5 seconds (count five seconds for each mile)

Pitch Pitch – frequency (not loudness) Audible range 20 Hz – 20,000 Hz InfrasonicAudibleUltrasonic 20 Hz 20,000 Hz Earthquakes50,000 Hz (dogs) Thunder100,000Hz(bats) Volcanoes Machinery

Intensity Intensity = Loudness Louder = More pressure Decibel (dB) – named for Alexander Graham Bell Logarithmic scale Intensity level = 

 = 10 log I I o I o = 1.0 X W/m 2 = lowest audible intensity

Example Rustle of leaves = 10 dB Whisper = 20 dB Whisper is 10 times as intense Example Police Siren = 100 dB Rock Concert = 120 dB

Decibels: Example 1 How many decibels is a sound whose intensity is 1.0 X W/m 2 ?  = 10 log I=10 log (1.0 X W/m 2 ) I o (1.0 X W/m 2 )  = 10 log (100) = 20 dB

Decibels: Example 2 What is the intensity of a conversation at 65 dB  = 10 log I I o  = log I 10 I o 65 = log I 10 I o

6.5 = log I I o 6.5 = log I – log I o log I = log I o log I = log (1.0 X W/m 2 ) log I = 6.5 – 12 = -5.5 I = = 3.16 X 10 -6

Decibels: Example 3 What is the intensity of a car radio played at 106 dB? (Ans: 1.15 X W/m 2 )

Decibels: Example 4 A blender produces an intensity level of 83dB. Calculate the decibels if a second blender is turned on (doubles the intensity, I o = 1.0 X W/m 2 ).

Intensity and Distance Intensity = Power/area Inverse-squared radius Intensity decreases proportionally as you move away from a sound (area of a ripple increases as you move out) I  1orI 1 r 1 2 = I 2 r 2 2 r 2

Distance: Example 1 The intensity level of a jet engine at 30 m is 140 dB. What is the intensity level at 300 m? 140 dB = 10 log I/I o 14 = log I/I o 14 = log I – log I o log I = 14 + log I o = 2 I = 100 W/m 2

I 1 r 1 2 = I 2 r 2 2 I 2 = I 1 r 1 2 /r 2 2 I 2 = (100 W/m 2 )(30 m) 2 /(300 m) 2 I 2 = 120 dB

Distance: Example 2 If a particular English teacher talks at 80 dB when she is 10 m away, how far would you have to walk to reduce the sound to 40 dB? (Hint: Find the raw intensity of each dB first). ANS: 1000 m

Doppler Effect Frequency of sound changes with movement Moving towards you = frequency increases (higher pitch) Moving away = frequency decreases (lower frequency)

Moving Source Source moving towards stationary observer f’ = f 1 - v s v Source moving away from stationary observer f’ = f 1 + v s v

Moving Observer Observer moving towards stationary source f’ = 1 + v o f v Observer moving away from stationary source f’ = 1 - v o f v

Doppler Effect and the Universe Universe is expanding Evidence (Hubble’s Law) –Only a few nearby galaxies are blueshifted –Most are red-shifted Universe will probably expand forever

Doppler: Example 1 A police siren has a frequency of 1600 Hz. What is the frequency as it moves toward you at 25.0 m/s? f’ = f 1 - v s v f’ = 1600 Hz = 1600 Hz = 1726 Hz [1 – (25/343)] 0.927

What will be the frequency as it moves away from you? f’ = f 1 + v s v f’ = 1600 Hz = 1600 Hz = 1491 Hz [1 + (25/343)] 1.07

Doppler: Example 2 A child runs towards a stationary ice cream truck. The child runs at 3.50 m/s and the truck’s music is about 5000 Hz. What frequency will the child hear? f’ = 1 + v o f v

v f’ = [1+(3.50/343)]5000 Hz f’ = (1.01)(5000 Hz) = 5051 Hz

Electromagnetic (EM) Waves Can travel through space Radio, Microwaves, IR, Light, UV, X-rays, Gamma Rays All on the electromagnetic spectrum James Clerk Maxwell

EM Wave Sinusoidal E and B are perpendicular to one another E and B are in phase Accelerating electric charges produce electromagnetic waves

Wave Properties First man-made EM waves detected by Hertz (8 years of Maxwell’s death) = wavelength (meters) f = frequency (cycles/s or Hertz) c = f  (in a vacuum, c = 3.00 X 10 8 m/s)

3. Electromagnetic Spectrum Light Radio Radar MicroIR Visible Light UVX- rays Gamma

Visible light 4 X m to 7X m (400 to 700 nm) Electrons –Radio – running electrons up and down an antenna –Electrons moving within atoms and molecules –X-rays - Electrons are rapidly decellerated by striking metal Gamma Rays – Nuclear decay

Waves: Ex 1 Calculate the wavelength of a 60 Hz EM wave f  = c = c/f = (3.0 X 10 8 m/s)/60 s -1 = 5 X 10 6 m What range of the spectrum is this?

Waves: Ex 2 Calculate the wavelength of a 93.3 MHz FM radio station f  = c = c/f = (3.0 X 10 8 m/s)/(93.3 X 10 6 s -1 ) = 3.22 m

Waves: Ex 3 Calculate the frequency of 500 nm blue light. f  = c f  = c/  f = (3.0 X 10 8 m/s)/500 X m = 6 X Hz

Waves: Ex 4 When you speak to a telephone to someone 4000 km away, how long does it take the sound to travel? v = d/t t = d/v T = (4000 X 10 3 m)/(3 X 10 8 m/s) = 1.3 X10 -2 s Speed is less because of wires

Index of Refraction Light slows when passing through a substance Must be absorbed and re-emitted Eyes slow light by ~30% Bose-Einstein condensate (50 nanokelvins) v = 38 mph

n = c v v = speed in material n = index of refraction

Refraction: Ex 1 Calculate the speed of light in water n = c v v = c/n v = (3.00 X 10 8 m/s)(1.33) = 2.26 X 10 8 m/s